Without damaging the backsplash? Difficult but maybe. Will your new counters be the same thickness as the old? Maybe not, in which case, you'd probably need a new backsplash anyway.

Never count on that. Ykulll probably have to replace at least a few tiles and maybe install a liner tile to compensate for thickness. You can’t make an omelette without breaking eggs.

My quartz installer was able to remove my laminate counters without breaking any of the original 20 year old 4x4 backsplash tiles. I don't know how they were able to do it!

There is a 1/4" difference between the new quartz and the old laminate, with the laminate being taller. I was going to keep the backsplash but I decided to get a new one.